Banana french toast

My son likes french toast.
When he was studying in boston, he had gone a couple of times to this place called Zaftig;s in brookline. They had a banana french toast that he particularly liked. I tried it and thought it was no big deal and thought I could make something better.

Anyway, this morning he was going to make himself some french toast and being half an italian mother, after all, I said let me make it. I also wanted to try out this idea that i had brewing.

I sliced two thinnish slices of my home made almost-no-knead bread (I don;t like french toast with soft or sweet bread, i think french toast requires some body)

I sliced half a banana in lenghthwise slices.

Soaked the bread on both sides in egg and a little milk and a sprinkle of salt.

I put the banana between the slices, leaving a border where the eggy bread would touch the eggy bread so it would hopefully cook together and keep the banana from leaking out. (It did work).

I heated the frying pan. added a chunk of butter, and when the foam subsided added the banana sandwich.
Put a little parchment paper on top and covered it with a small flat cover that would press it down a little (to be sure the egg would cook inside)
When it was done, removed to a plate.

but the brilliant idea was to make a sauce

the sauce
I took a sprinkle, maybe tbsp, of dark brown sugar, about the same of water (my brown sugar is raw and lumpy and crumbly but very tasty, but needed the water to dissolve it.
Added a chunk of butter (maybe a tbsp?)
A squeeze of lime juice.
cooked it down a little not to really caramelize it, but to make it slightly syrupy, and added maple syrup (couple of tbsp, maybe more) and sliced the rest of the banana into it. Cooked till the banana was softened a little, a bit less white looking, and poured it over the french toast.
Voila'!
it was really good. He said, with surprise, better than Zaftig's. No surprise to me.
Let me know if you try it.

Actually i added the maple syrup because my son likes it in particular. I think it would be fine with just brown sugar and water and banana.
Personally I wouldn't use ice cream - too many very sweet things together. I would use whipped cream if i wanted to dessertify it - because it would kind of cut the sweetness but add a touch of creaminess. Slightly sweetened with a little vanilla in it. I guess it would be like a kind of bread pudding then.